Expand two counters in collect package

Question

I write a command to store the problem answer with the collect package. Mr @egreg help me expand the problem number in the aux file. Now I meet another trouble with the answer. When the answer contains a counter, it will not expand. Please help me correct the below code.

Moreover, please give some documentation of "expandafter" and ".aux" commands Thank you very much!

\documentclass{article}
\usepackage{collect}
\definecollection{btcol}
\newcounter{cbt} %the number problems
\newcounter{anschoice} %the answer key
\newenvironment{bt}
 {\refstepcounter{cbt}\par
  \noindent{\bfseries Problem \thecbt}.}{}
\makeatletter
\newcommand{\loigiai}[1]{%
  @bsphack\expandafter\loigiai@aux\expandafter{\expanded{\thecbt}}{#1}@esphack
}
\newcommand{\loigiai@aux}[2]{%
  \begin{collect}{btcol}{\par\noindent {\bfseries AP #1}.\ignorespaces}{}{}{} 
#2%
  \end{collect}
}
\makeatother
\begin{document}
\setcounter{anschoice}{3}
\begin{bt}
Content 1
\loigiai{Answer for Pro.1 $ \rightarrow $ Choice: \Alph{anschoice}}
\end{bt}
\begin{bt}
Content 2 
\end{bt}
\setcounter{anschoice}{2}
\begin{bt}
Content 3
\loigiai{Answer for Pro.3  $ \rightarrow $ Choice: \Alph{anschoice}}
\end{bt}
\includecollection{btcol}
\end{document}

Answer 1

I'm sure this could be better automated, but here, I expand the offending phrase with an \edef, before passing it to \loigiai.

EDITED to simplify input for the user. Instead of forcing an \edef upon the user, I create the macro \exloigiai which the user may alternatively use, which applies \expanded to the argument prior to passing it to \loigiai.

\documentclass{article}
\usepackage{collect}
\definecollection{btcol}
\newcounter{cbt} %the number problems
\newcounter{anschoice} %the answer key
\newenvironment{bt}
 {\refstepcounter{cbt}\par
  \noindent{\bfseries Problem \thecbt}.}{}
\makeatletter
\newcommand{\loigiai}[1]{%
  @bsphack\expandafter\loigiai@aux\expandafter{\expanded{\thecbt}}{#1}@esphack
}
\newcommand{\loigiai@aux}[2]{%
  \begin{collect}{btcol}{\par\noindent {\bfseries AP #1}.\ignorespaces}{}{}{} 
#2%
  \end{collect}
}
\newcommand\exloigiai[1]{\expandafter\loigiai\expandafter{\expanded{#1}}}
\makeatother
\begin{document}
\setcounter{anschoice}{3}
\begin{bt}
Content 1
\exloigiai{Answer for Pro.1 $ \rightarrow $ Choice: \Alph{anschoice}}
\end{bt}
\begin{bt}
Content 2 
\end{bt}
\setcounter{anschoice}{2}
\begin{bt}
Content 3
\exloigiai{Answer for Pro.3 $ \rightarrow $ Choice: \Alph{anschoice}}
\end{bt}
\includecollection{btcol}
\end{document}